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Cell[CellGroupData[{
Cell["\<\

Experimental Investigation of the Spectral Radius of the Jacobian Relaxation \
Operator for Laplace's Equation and the Resultant Succesive Overrelaxation \
Parameter\
\>", "Title"],

Cell["Fit of Iteration as a Function of Grid Size", "Subtitle"],

Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
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        iter\  = \ {{20, 163}, {30, 352}, {40, 606}, {50, 923}, {60, 
          1301}, \ {70, \ 1739}, \ {100, \ 3401}, \ {120, \ 4789}, \ {140, \ 
          6394}}\)], "Input"],

Cell[BoxData[
    \({{20, 163}, {30, 352}, {40, 606}, {50, 923}, {60, 1301}, {70, 
        1739}, {100, 3401}, {120, 4789}, {140, 6394}}\)], "Output"]
}, Open  ]],

Cell["\<\
this was run with boundaries 0,1,0,0 on the region [0,1]*[0,1]\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(iter\  = {{20, 291}, {30, 581}, {40, 940}, {50, 1357}, {60, 
          1821}, \ {70, \ 2325}, \ {100, \ 4019}, \ {120, \ 5249}, \ {140, \ 
          6696}, {200, 12639}}\)], "Input"],

Cell[BoxData[
    \({{20, 291}, {30, 581}, {40, 940}, {50, 1357}, {60, 1821}, {70, 
        2325}, {100, 4019}, {120, 5249}, {140, 6696}, {200, 
        12639}}\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Calculation of the Spectral Radius", "Subtitle"],

Cell[CellGroupData[{

Cell[BoxData[
    \(\[Rho]nm[J_]\  = \ 1 - \[Pi]\^2\/J\^2\)], "Input"],

Cell[BoxData[
    \(1 - \[Pi]\^2\/J\^2\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(\[Rho][p_, r_]\  = \ 1\/10\^\(p\/r\)\)], "Input"],

Cell[BoxData[
    \(10\^\(-\(p\/r\)\)\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(experiment\  = 
      Table[{\(iter[\([i]\)]\)[\([1]\)], 
          N[\[Rho][5, \(iter[\([i]\)]\)[\([2]\)]]]}, \ {i, \ 1\ , 
          Length[iter]}]\)], "Input"],

Cell[BoxData[
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        0.9971394747210545`}, {120, 0.9978090476816315`}, {140, 
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Cell[CellGroupData[{

Cell[BoxData[
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      Table[{\(iter[\([i]\)]\)[\([1]\)], 
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          Length[iter]}]\)\(\[IndentingNewLine]\)
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Cell[BoxData[
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        0.9990130395598911`}, {120, 0.9993146108054799`}, {140, 
        0.9994964487550465`}, {200, 0.9997532598899728`}}\)], "Output"]
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Cell[CellGroupData[{

Cell[BoxData[
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        PlotJoined\  \[Rule] \ 
          True, \ \ PlotRange\  \[Rule] \ {{0, \ jmax}, Automatic}]\n
    theoryPlot := 
      ListPlot[theory, \ 
        PlotJoined\  \[Rule] \ 
          True, \ \ PlotRange\  \[Rule] \ {{0, \ jmax}, Automatic}, \ 
        PlotStyle\  \[Rule] \ Hue[1]]\n
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Cell["Spectral Radius for the Simple Harmonic Oscillator", "Title"],

Cell["experimentally determined spectral radii", "Subtitle"],

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